The $11$-element case of Frankl's conjecture

  • Ivica Bošnjak
  • Petar Marković

Abstract

In 1979, P. Frankl conjectured that in a finite union-closed family ${\cal F}$ of finite sets, ${\cal F}\neq\{\emptyset\}$, there has to be an element that belongs to at least half of the sets in ${\cal F}$. We prove this when $|\bigcup{\cal F}|\leq 11$.

Published
2008-07-06
Article Number
R88